Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+4y &= -4 \\ 5x+4y &= -8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -4y-8$ Divide both sides by $5$ to isolate $x$ $x = {-\dfrac{4}{5}y - \dfrac{8}{5}}$ Substitute this expression for $x$ in the first equation. $-4({-\dfrac{4}{5}y - \dfrac{8}{5}}) + 4y = -4$ $\dfrac{16}{5}y + \dfrac{32}{5} + 4y = -4$ Simplify by combining terms, then solve for $y$ $\dfrac{36}{5}y + \dfrac{32}{5} = -4$ $\dfrac{36}{5}y = -\dfrac{52}{5}$ $y = -\dfrac{13}{9}$ Substitute $-\dfrac{13}{9}$ for $y$ in the top equation. $-4x+4( -\dfrac{13}{9}) = -4$ $-4x-\dfrac{52}{9} = -4$ $-4x = \dfrac{16}{9}$ $x = -\dfrac{4}{9}$ The solution is $\enspace x = -\dfrac{4}{9}, \enspace y = -\dfrac{13}{9}$.